K-12 Louisiana Student Standards for Mathematics: Table of Contents Introduction Development of K-12 Louisiana Student Standards for Mathematics .................................................. 2 The Role of Standards in Establishing Key Student Skills and Mathematical Proficiency ..................... 2 Structure of the Standards .................................................................................................................. 2 Reading Standards and Interpreting their Codes in Grades 3-8 ........................................................... 3 Reading Standards and Interpreting their Codes in High School Courses ............................................ 4 Companion Documents for Teachers ................................................................................................... 5 Progressions in the Math Standards .................................................................................................... 5 Louisiana Student Standards for Mathematics Standards for Mathematical Practice ................................................................................................. 6 Standards for Mathematical Content by Grade Kindergarten .............................................................................................................................. 9 Grade 1 .................................................................................................................................... 12 Grade 2 .................................................................................................................................... 15 Grade 3 .................................................................................................................................... 18 Grade 4 .................................................................................................................................... 22 Grade 5 .................................................................................................................................... 26 Grade 6 .................................................................................................................................... 30 Grade 7 .................................................................................................................................... 35 Grade 8 .................................................................................................................................... 39 Algebra I ................................................................................................................................... 43 Geometry ................................................................................................................................. 48 Algebra II .................................................................................................................................. 52 Glossary and Tables .................................................................................................................. 57 Resources Instructional Materials Resources ..................................................................................................... 63 Standards by Domain: Kindergarten through Grade 8 ....................................................................... 63 Teachers Companion Documents ...................................................................................................... 63 Remediation Guides .......................................................................................................................... 64 Updated December 21, 2017 (edited 5.MD.C.5b and 6.G.A.2 to use capital B) 1 K-12 Louisiana Student Standards for Mathematics: Introduction Introduction Development of K-12 Louisiana Student Standards for Mathematics The Louisiana mathematics standards were created by over one hundred Louisiana educators with input by thousands of parents and teachers from across the state. Educators envisioned what mathematically proficient students should know and be able to do to compete in our society and focused their efforts on creating standards that would allow them to do so. The new standards provide appropriate content for all grades or courses, maintain high expectations, and create a logical connection of content across and within grades. The Role of Standards in Establishing Key Student Skills and Mathematical Proficiency Students in Louisiana are ready for college or a career if they are able to meet college and workplace expectations without needing remediation in mathematics skills and concepts. The standards define what Louisiana students should know, understand, and be able to do mathematically and represent the steps students must take along the way to be able to meet this goal. For example, all students should be able to recall and use math skills and concepts on a daily basis. That is, a student should know certain math facts and concepts such as how to add, subtract, multiply, and divide basic numbers with ease, how to work with simple fractions and percentages, and how to apply basic algebra and geometry principles. Additionally, students need to be able to reason mathematically, communicate with others about math through speaking and writing, and problem solve in real-world situations to be prepared mathematically for post-secondary education or to pursue a career. The K-12 mathematics standards lay the foundation that allows students to become mathematically proficient by focusing on conceptual understanding, procedural skill and fluency, and application. Conceptual understanding refers to understanding mathematical concepts, operations, and relations. It is more than knowing isolated facts and methods. Students should be able to make sense of why a mathematical idea is important and the kinds of contexts in which it is useful. It also allows students to connect prior knowledge to new ideas and concepts. Procedural Skill and Fluency is the ability to apply procedures accurately, efficiently, and flexibly. It requires speed and accuracy in calculation while giving students opportunities to practice basic skills. Students’ ability to solve more complex application tasks is dependent on procedural skill and fluency. Application provides a valuable context for learning and the opportunity to solve problems in a relevant and a meaningful way. It is through real-world application that students learn to select an efficient method to find a solution, determine whether the solution(s) makes sense by reasoning, and develop critical thinking skills. Structure of the Standards There are two types of standards in the Louisiana Mathematics Standards – mathematical practice and content. A summary of each type is provided below: 1. Standards for Mathematical Practice – Apply to all grade levels – Describe mathematically proficient students 2. Standards for Mathematical Content – K-8 standards presented by grade level – High school standards presented by high school course (Algebra I, Geometry, Algebra II), then organized by conceptual categories: • Number and Quantity • Modeling • Algebra • Geometry • Functions • Statistics and Probability 2 K-12 Louisiana Student Standards for Mathematics: Introduction The following terms will assist in understanding how to read the content standards and their codes. Terms are defined in order from most specific to most general. Standards - Statements of what a student should know, understand, and be able to do. Clusters - Groups of related standards. Cluster headings may be considered as the big idea(s) that the group of standards they represent are addressing. Cluster headings are therefore useful as a quick summary of the progression of ideas that the standards in a domain are covering and can help teachers to determine the focus of the standards they are teaching. Domains - A large category of mathematics that the clusters and their respective content standards delineate and address. For example, Number and Operations – Fractions is a domain under which there are a number of clusters (the big ideas that will be addressed) along with their respective content standards, which give the specifics of what the student should know, understand, and be able to do when working with fractions. Conceptual Categories – The content standards, clusters, and domains in Algebra I, Geometry, and Algebra II are further organized under conceptual categories. These are very broad categories of mathematical thought and lend themselves to the organization of high school course work. For example, Algebra is a conceptual category in the high school standards under which are domains such as Seeing Structure in Expressions, Creating Equations, Arithmetic with Polynomials and Rational Expressions, etc. Reading Standards and Interpreting their Codes in Grades K-8 Example from the Grade 3 standards: There are four parts to the code for a mathematics standard in Kindergarten through Grade 8. The Cluster Headers are identified by an uppercase letter (A, B, C…). If a Domain has four clusters, then the letter A is assigned to the heading for the first cluster, B to the second, C to the third, and D to the fourth cluster. Each part of the code is separated by a period and has a specific meaning: PART ONE PART TWO PART THREE PART FOUR Grade Level Domain Cluster Standard # Look at the example below. It is the code for the last Grade 3 standard in the above list. 3.NBT.A.3 The grade level is 3, the domain code is NBT (Numbers and Operations in Base Ten), the cluster is A (first cluster),